Abstract
In this paper, the Lie group theory is used to estimate the position and attitude of a mobile robot. In the proposed method, a Kalman filter (KF) is implemented in a Lie group, specifically in a two-dimensional special Euclidean group SE(2). Position and attitude are represented as variables in SE(2). State transition is modeled using the exponential of the Lie algebra se(2) , which corresponds to SE(2) . Covariance of the estimates and correction of the predicted state are calculated using Lie algebra se(2). The performance of the proposed method is tested by conducting a simulation and is compared with the conventional extended KF, where Cartesian space coordinates and heading angle are used as state variables. The test results verify that the proposed method provides estimates that have smaller errors than those provided by the conventional extended KF. The Kalman gain and measurement innovation of the proposed method have superior convergence performance than the usual extended KF.
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